Future space missions such as the Earth Science Geostationary Platform (ESGP) will require highly accurate antennas with apertures that cannot be launched fully formed. The operational orbits are often inaccessible to manned flight and will involve expendable launch vehicles such as the Delta or Titan. There is therefore a need for completely deployable antenna reflectors of large size capable of efficiently handling millimeter wave electromagnetic radiation. The parameters for the type of mission are illustrated. The logarithmic plot of frequency versus aperture diameter shows the regions of interest for a large variety of space antenna applications, ranging from a 1500-meter-diameter radio telescope for low frequencies to a 20-meter-diameter infrared telescope. For the ESGP, a major application is the microwave radiometry at high frequencies for atmospheric sounding. Almost all existing large antenna reflectors for space employ a mesh-type reflecting surface. Examples are shown and discussed which deal with the various structural concepts for mesh antennas. Fortunately, those concepts are appropriate for creating the very large apertures required at the lower frequencies for good resolution. The emphasis is on the structural concepts and technologies that are appropriate to fully automated deployment of dish-type antennas with solid reflector surfaces. First the structural requirements are discussed. Existing concepts for fully deployable antennas are then described and assessed relative to the requirements. Finally, several analyses are presented that evaluate the effects of beam steering and segmented reflector design on the accuracy of the antenna.